Arrange the following in decreasing order of the pK value:

(A) \(C_2H_5NH_2\)

(B) \(C_6H_5NHCH_3\)

(C) \((C_2H_5)_2NH\)

(D) \(C_6H_5NH_2\)

(E) \((CH_3)_3N\)

Choose the correct answer from the options given below:

\(C_6H_5NH_2 > C_6H_5NHCH_3 >(CH_3)_3N > C_2H_5NH_2 > (C_2H_5)_2NH\)

The correct answer is option 3. \(C_6H_5NH_2 > C_6H_5NHCH_3 >(CH_3)_3N > C_2H_5NH_2 > (C_2H_5)_2NH\).

To determine the decreasing order of pK values for the given compounds, we need to consider their basicity. Generally, compounds with higher pK values have weaker basicity, while those with lower pK values have stronger basicity.

Here's a breakdown of the compounds provided:

(A) \(C_2H_5NH_2\) - Ethylamine

(B) \(C_6H_5NHCH_3\) - N-Methylaniline

(C) \((C_2H_5)_2NH\) - Diethylamine

(D) \(C_6H_5NH_2\) - Aniline

(E) \((CH_3)_3N\) - Trimethylamine

Now, let's arrange them in decreasing order of pK values based on their basicity:

1. \(C_6H_5NH_2\) (Aniline) - Aniline is less basic compared to alkylamines due to the delocalization of the lone pair of electrons into the benzene ring, which reduces its availability for donation to a proton. Hence, it has a higher pK value.

2. \(C_6H_5NHCH_3\) (N-Methylaniline) - The presence of a methyl group increases the electron density on the nitrogen atom, making it slightly more basic than aniline but still less basic than alkylamines.

3. \((CH_3)_3N\) (Trimethylamine) - Trimethylamine is a stronger base compared to aniline and N-methylaniline due to the presence of three alkyl groups, which further increases the electron density on the nitrogen atom.

4. \(C_2H_5NH_2\) (Ethylamine) - Ethylamine is a stronger base compared to aniline and N-methylaniline due to the presence of an alkyl group, which increases the electron density on the nitrogen atom.

5. \((C_2H_5)_2NH\) (Diethylamine) - Diethylamine is a stronger base compared to ethylamine due to the presence of two alkyl groups, which further increases the electron density on the nitrogen atom.

Based on this analysis, the decreasing order of pK values is: \(C_6H_5NH_2 > C_6H_5NHCH_3 > (CH_3)_3N > C_2H_5NH_2 > (C_2H_5)_2NH\)

So, the correct answer is option (3) \(C_6H_5NH_2 > C_6H_5NHCH_3 >(CH_3)_3N > C_2H_5NH_2 > (C_2H_5)_2NH\).